Why Philosophy of Physics?

Philosophy of Physics today is largely Philosophy of Quantum Mechanics PQM struggling to give meaning to a QM formed 100 years ago by physicists as modern physics without clear physical meaning. 

PQM then has the double role of (i) cover up lack of meaning and (ii) expose lack of meaning. In either case PQM has a difficult task, which rarely can be pursued at a physics department and so may rather be part of a department of philosophy without physics. Here (ii) invites the critical mind to easy catches, while (i) to be successful requires clever argumentation. 

In both cases the real problem of finding a form of QM with physical meaning is left aside and no progress will take place. The result is that none of the questions about the physical meaning of Schrödinger's equation, formulated in 1926 and still serving as the basis of QM, has been given an answer accepted by the physics community. 

Here RealQM may have something meaningful to offer as a mathematical model of the form of continuum mechanics in physical 3d space with clear ontology. If indeed RealQM does show to function as a physical model of atoms and molecules, then PQM will face a new situation without need to take care of (i)+(ii), and so will have to find a new role, maybe as a challenge to philosophers. 

Leibniz's PII vs RealQM vs StdQM

Leibniz's Principle of the Identity of Indiscernibles PII clashes with the basic idea of identical particles of textbook StdQM: If the electrons of a molecule are identical, that is indiscernible, then they would according to Leibniz be identical and so there would be only one electron present, maybe then in the form of a super-electron distributed over the molecule? 

Leibniz today would object to the idea of identical electrons of StdQM, and so would welcome RealQM where electrons have identity/individuality by occupying separate regions in space with continuity in time. 

Electron individuality has a special role in RealQM with Coulomb repulsion present only between charge densities of different electrons, not within individual charge densities. 

But without individuality, lack of self-repulsion cannot be safely built in, which means that in StdQM self-repulsion has to be actively removed as exchange, which presents a major difficulty.

Recall that the electronic wave-functions of StdQM are required to be anti-symmetric,  that is change sign under swapping of electron labels, while labelling of identical electrons appears as strange as well as sign change without reason. 

Why Philosophy of Chemistry?

This is a comment to the previous post on submission of a RealQM article to Foundations of Chemistry edited by Eric Scerri founder of the 21st century discipline Philosophy of Chemistry. 

What can be the role of a philosophy of chemistry? Why was it formed only recently? To seek answers we ask chatGPT to take on both a defensive and a critical attitude and ask about the role of Quantum Mechanics QM as foundation of chemistry, to get the following condensed answer:

Defense (QM as a strong foundation)

Quantum mechanics is the fundamental theory governing electrons and nuclei, so all chemical phenomena ultimately arise from it. Atoms, bonds, spectra, and periodic trends are, in principle, consequences of quantum laws. Chemical concepts (orbitals, bonds, valence) are higher-level descriptions of underlying quantum reality. Quantum chemistry shows that structures, energies, and reactions can be derived from first principles, even if approximations are needed in practice. Thus, chemistry is autonomous in use but reducible in principle to QM.

---

Critique (QM as a limited foundation)

Quantum mechanics constrains what is physically possible, but it does not supply the concepts chemistry depends on. Molecular structure, bonds, functional groups, and mechanisms are not contained in the fundamental equations and must be imposed through approximations and conventions. QM provides calculations, not chemical explanations; multiple quantum descriptions can map onto the same “structure,” showing underdetermination. Quantum chemistry relies on chemical input and interpretation rather than replacing chemical reasoning. Thus, QM is necessary but not sufficient: chemistry remains conceptually and explanatorily autonomous.

 New prompt: Is the role of philosophy of chemistry to handle the contradiction between the two statements?

chatGPT: The philosophy of chemistry addresses the apparent contradiction by clarifying what “based on” means. It distinguishes physical dependence from theoretical reduction and explanatory grounding, showing that chemistry can obey quantum laws without being conceptually derived from them. It analyzes reduction versus emergence, evaluates what counts as explanation, and studies actual scientific practice in quantum chemistry and laboratory work. In doing so, it reframes the conflict: quantum mechanics underwrites chemistry at the physical level, while chemistry retains autonomy in its concepts and explanations.

Summary: We find that a main role of Philosophy of Chemistry is to handle two contradictory views on the functionality of QM as foundation of chemistry. RealQM appears to offer a new foundation with new functionality, where there is no contradiction, and if successful will reduce the need of philosophy to reconcile contradictions.

 

First Submission of RealQM Article

The first of a series of articles about RealQM has been submitted to Foundations of Chemistry with here an updated version:

• Alternative Computational Foundation of Chemistry    (download to get active hyperlinks)

A basic idea is to view formation of a molecule as a form of dynamic analog computation seeking balance of physical forces which can be simulated by digital computation in a new Schrödinger equation with linear computational complexity of the form of classical multi-phase continuum mechanics. This offers a foundation of chemistry as computational mathematical physics.  

RealQM is to be compared with textbook QM based on a multi-dimensional Schrödinger equation with exponential computational complexity. 

Is Chemistry Explained by Quantum Mechanics?

Here are some quotes by famous chemists connecting to the previous post on RealQM as an alternative to textbook StdQM: 

• The great enabler of chemistry, quantum mechanics, also reveals the poverty of our language and concepts. (Roald Hoffmann)
• There is no unique way of defining a chemical bond from quantum mechanics. (Roald Hoffmann)
• The concepts of chemistry are more than the consequences of the Schrödinger equation. (Linus Pauling)
• The concept of the chemical bond is not a real one; it is a figment of our own imagination. A bond does not exist as an observable entity.( Charles Coulson)
• Quantum mechanics does not provide a definition of a chemical bond. (Richard Bader)
• Quantum Mechanics supplies numbers, chemistry supplies meaning. (Henry Eyring)
• Theories of physics cannot explain the principles governing chemical reactions. (Michael Polanyi)
• The exact solution of the Schrödinger equation would not solve the chemical problem. (Per-Olov Löwdin)
• Orbitals, bonds, and structures are models imposed on quantum results, not entities delivered by QM itself. (John C. Slater)
• The chemical bond is not a quantum-mechanical observable. (George C. Pimentel)
• Chemistry is not derivable from quantum mechanics in any straightforward sense. (Hans Primas)
• Orbitals are not physical realities; they are mathematical constructs. (Robert S. Mulliken)
• The microscopic description does not exhaust the meaning of macroscopic phenomena. (Ilya Prigogine)
• Exact quantum dynamics would still not yield chemical concepts such as mechanisms, bonds, or reaction pathways. (William H. Miller)
• Quantum mechanics does not directly provide chemical structure; structure is inferred. (Jerome Karle)
• Quantum numbers and wave functions do not by themselves define chemical individuality. (Friedrich Hund)
• Quantum mechanics explains everything in principle, but nothing in practice — and very little in concept. QM does not define chemical bonds. QM does not uniquely explain molecular structure. Chemical explanation involves conceptual frameworks not present in physics. Chemistry is not simply applied quantum mechanics. Quantum mechanics is indispensable to chemistry, yet insufficient as a chemical explanation. (Consensus)

Compare with what famous physicists claim:

• Quantum electrodynamics is the most accurate theory we have ever had. (Richard Feynman)
• Quantum mechanics is surely the most successful physical theory we have ever discovered. (Steven Weinberg)
• The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known. (Paul Dirac)
• Quantum electrodynamics is the most accurate theory known to man. (Julian Schwinger)
• No experimental result has ever contradicted quantum mechanics. (Max Born)
• Quantum mechanics works astonishingly well—better than we have any right to expect. (Frank Wilczek)
• Quantum mechanics is not just correct; it is spectacularly correct. (Sean Carroll)
• Quantum theory has survived every experimental test to which it has been subjected. (David Deutsch)
• The predictions of quantum mechanics are so spectacularly confirmed that it is hard to contemplate abandoning it. (John Bell)
• Quantum mechanics is the most successful predictive framework ever developed, unmatched in accuracy, scope, and experimental confirmation. (Consensus)

Draw your own conclusion.

Mathematical Foundation of Chemistry?

Let us start the 2026 Anniversary Year of Schrödinger's equation by asking about the role of Mathematics in Chemistry.  

August Comte in his Cours de Philosophie Positive (1830-42) stated

• All attempts to bring chemical questions into the domain of mathematics must be regarded as profoundly irrational, and antipathetic to the nature of these phenomena. 

This cannot be true today, right? Mathematical physicists like Dirac already 90 years ago claimed that chemistry is only a branch of applied atomic physics, which is fully described by Schrödinger/Dirac's differential equation as the mathematical model of textbook Standard Quantum Mechanics StdQM, with the only little caveat that analytical solutions are unknown and numerical solutions are only available in drastically simplified form.  

The result is that physicists today say that chemistry is explained by StdQM, in principle, while chemists facing reality see that chemical bonding is not well explained, because it is not within the scope of StdQM as being restricted to energies leaving out forces. 

If you want to find some hope as a chemist or layman, take a look at this new article:    

• Alternative Computational Foundation of Chemistry

where computational mathematics and real physics are seen to merge into explanations. 

Comment by chatGPT on prompt: Give comment to this text:

This article presents an ambitious and provocative proposal—RealQM—as an alternative computational and conceptual foundation for quantum chemistry. Its central idea, modeling electrons as non-overlapping charge densities in real three-dimensional space with a free-boundary formulation, is original and intellectually stimulating. The work stands out for its explicit dissatisfaction with the interpretational and computational burdens of Standard Quantum Mechanics (StdQM) and for attempting to restore locality, physical intuition, and linear computational scaling.

Strengths and contributions

1. Clear ontological stance
   The paper adopts a consistently realist ontology, treating electron densities as physical objects rather than probabilistic constructs. This addresses a long-standing discomfort many chemists and physicists have with the configuration-space formalism of StdQM and aligns with Schrödinger’s original intuitions.

2. Computational motivation
   The emphasis on linear scaling with the number of electrons and the reduction to a “three-line code” is compelling. If robust, this would represent a genuine breakthrough for ab initio simulations, particularly for large systems where StdQM-based methods require severe approximations.

3. Unified continuum framework
   Casting atomic and molecular structure as a multi-phase continuum mechanics problem with free boundaries is mathematically elegant and conceptually coherent. The analogy with classical variational principles and gradient flows is one of the paper’s strongest aspects.

4. Concrete demonstrations
   The article goes beyond philosophical critique by presenting numerical results for atoms, molecules, shell structure, bonding, and even speculative nuclear models. This breadth is unusual and commendable.

Points requiring clarification or strengthening

1. Status of non-overlap and exclusion
   The assumption of non-overlapping electron densities replaces Pauli exclusion, antisymmetry, and spin with geometric separation. While this is internally consistent, the paper would benefit from a clearer argument explaining why non-overlap is physically justified rather than merely effective. At present, it risks being perceived as a built-in constraint that substitutes, rather than explains, fermionic behavior.

2. Empirical scope and validation
   Agreement with selected ground-state energies is encouraging, but chemistry is ultimately judged by predictive power across a wide range of observables: excitation spectra, reaction barriers, response properties, magnetic effects, and spin-dependent phenomena. The absence of spin, exchange, and correlation needs to be addressed not only philosophically but also empirically.

3. Excited states and spectroscopy
   The discussion of excited states and radiation via beat frequencies is intriguing, but it remains qualitative. It is unclear whether RealQM can systematically reproduce selection rules, fine structure, or multiplet splittings that are central to atomic and molecular spectroscopy.

4. Free-boundary dynamics and uniqueness
   The Bernoulli free-boundary formulation is central to the theory, yet questions of uniqueness, stability, and convergence of the boundary evolution are largely unaddressed. These issues are critical if RealQM is to be regarded as a well-posed physical theory rather than a numerical construction.

5. Polemic tone
   While the historical critique of StdQM is understandable, the repeated framing in terms of “brainwashing” and “non-physics” may alienate readers who would otherwise engage seriously with the model. A more neutral tone would strengthen the paper’s reception in the broader community.

Overall assessment

The article is bold, unconventional, and intellectually rich. It challenges deeply entrenched assumptions in quantum chemistry and offers a coherent alternative grounded in real-space physics and computability. Whether RealQM can ultimately replace or complement StdQM remains an open question, but the work deserves careful scrutiny rather than dismissal. At minimum, it functions as a valuable thought experiment that forces reconsideration of what is essential—and what may be contingent—in the quantum-mechanical description of chemistry.

If developed further with clearer empirical benchmarks, mathematical analysis of the free-boundary problem, and a more systematic treatment of excited-state phenomena, RealQM could stimulate productive debate well beyond its immediate claims.

Basic Mystery of Quantum: Shared vs Individual

The basic mystery of textbook Standard Quantum Mechanics StdQM serving as the foundation of modern physics, is the physical meaning of the wave function $\Psi (x_1,...,x_N)$ for a system with $N$ electrons depending on  $N$ spatial variables $x_1,...,x_N$ each $x_i$ serving as the 3d Euclidean coordinate of a copy $E_i$ of the same Euclidean space $E=\Re^3$, for $i=1,...,N$, with the total coordinate $x=(x_1,...,x_N)$ sweeping over configuration space as $\Re^{3N}$.

The mystery comes from the fact the each $E_i$ is connected to an electron $i$ and so serves as an individual universe for each electron. Very strange. The inspiration maybe came for the Monad Theory of Leibniz where each monad (as form of elementary unit like an electron) has its own universe to dwell in, while taking in blurred perceptions from all other monads.  

But electrons interact through Coulomb potentials 

• $\frac{1}{\vert x_i -x_j\vert}$ with $i\neq j$ 

which means that both $E_i$ and $E_j$ are identified with the same $E$, where the Coulomb interaction takes place.

We see that each $E_i$ serves a double role as both representing an individual and a common shared 3d space. Very confusing. 

The physics of QM has two elements:

1. Coulomb interaction between electrons in a common shared physical 3d space.
2. Kinetic energy from presence of a Laplacian acting in each individual $E_i$. 

Here 1 is shared and 2 individual and QM as the combination of 1 + 2 has to struggle to make sense of this contradictory mix. Ok?

Recall that StdQM is uncomputable because of the $3N$ spatial dimensions. 

RealQM is an alternative to StdQM formulated in terms of a wave function depending on a single physical variable in a 3d Euclidean space E. RealQM is computable because computational complexity scales linearly with $N$. 

It is a mystery that RealQM has been developed only recently, since it is very natural and does not suffer from the many unresolved issues of StdQM. Why not give it a try, after having struggled for 100 years to make sense of StdQM?

Ab Initio Computational Quantum Mechanics

The basic mathematical model of atomic physics according to textbook Standard Quantum Mechanics StdQM, is Schrödinger's Equation SE over a configuration space of $3N$ spatial dimensions for an atomic system with $N$ electrons. SE in atomic units is parameter-free and only contains case-specific data and so in principle allows ab initio prediction of physical reality without experimental determination of parameters, and so is an example of Kant's a priori as pure thought knowledge about the world without experimental input, by Einstein identified as the ideal.

But there is a fundamental caveat: SE has exponential computational complexity and so does not deliver any predictions unless $N$ is very small, and so the ideal is empty of content.

RealQM is a different atomic model based on non-overlapping one-electron charge densities in common physical 3d space with computational complexity scaling linearly in $N$, with mesh size as only parameter.

StdQM and RealQM are both based on the same parameter-free principles:

1. Coulomb interaction between charge densities.
2. Kinetic energy of charge densities measured by spatial gradients. 

The difference is that StdQM is formulated over $3N$-dimensional non-physical configuration space bringing exponential computational complexity, while RealQM is formulated over physical 3d space coming with linear computational complexity. StdQM in basic from is computable only for very small $N$, while RealQM is computable even for large $N$. 

In practice, StdQM is draconically dimensionally reduced into computable form by methods like Hartree-Fock and Density Functional Theory DFT including new parameters to be determined by experiment or experience, and so is no longer ab initio.

RealQM is computable in basic form with mesh resolution in 3d space as only parameter, and thus is truly ab initio, as a very remarkable fact. 

Macroscopic physics involves many parameters such as viscosity, conductivity, compressibility, elasticity and permeability emerging from microscopic physics. It is natural to expect microscopic physics to be  parameter-free, since otherwise microscopic physics would itself build on microscopic physics in an infinite regression. 

A parameter-free mathematical model is restricted in form and as is canonical. The list of computable ab initio models is short:

• The algebraic equation $x^2+y^2=1$ describing a circle of unit radius, from which the length of the circumference can be computed ab initio to be $2\pi $. More generally, Euclidean space captures all of geometry in parameter-free form.
• Newtonian mechanics captures all of celestial mechanics with normalised gravitational constant.
• Euler's equation for incompressible inviscid fluid flow allows computation of drag and lift of a body with the shape of the body as only input. 

To this list we can add RealQM covering all of non-relativistic Euclidean atom physics. 

Comment by chatGPT:

• Calling HF and DFT “ab initio” is a semantic maneuver that masks the absence of any scalable, derivable solution of the many-electron Schrödinger equation by rebranding uncontrolled closures—mean fields and unknown exchange–correlation functionals—as first principles rather than admitting a foundational failure of StdQM.

Modern Physics as Tragedy

In the beginning of the 20th century the science physics as the foundation of all of natural science, took a decisive step away from the principles of classical Newton-Maxwell continuum physics into a new era of  modern physics as atomic physics in the form of Quantum Mechanics QM combined with Einstein's General Relativity GR as a new theory gravitation replacing Newton's. 

So was modern physic created as QM + GR by breaking principles of classical physics opening new avenues while coming along with many problems which have never been resolved. 

A basic problem is that QM are GR incompatible and so do not together give physical theory covering all scales from atomic to galactic which must be the ultimate goal of a theory of physics. Something must be seriously wrong with either QM or GR. It is impossible that real atomic physics is incompatible with macroscopic physics built thereupon. 

The problem with GR is that it is based on two Postulates ("Relativity" and "Equivalence") both of which lack physical content.

Textbook Standard QM StdQM suffers from a similar problem on non-physicality because its basic mathematical model in the form of Schrödinger's Equation SE suffers from both lack of physical content and exponential computational complexity.  This means that the wave function $\Psi$ as solution to SE is not computable and so cannot reveal "everything there is to say about an atomic system", which is how modern physicists speak about $\Psi$. 

Yet QM is described as the basis of modern society with its computer chips, atomic bombs and now AI,  supported by a claim that no computed $\Psi$ has ever disagreed with experiment (which is trivially true because $\Psi$ is uncomputable).

Let us recall that Greek tragedy begins when the hero makes a critical error in judgment, because of

• hubris
• ignorance of crucial facts
• stubbornness

all of which can be found in the Copenhagen Interpretation CI of QM according to Bohr-Born-Heisenberg. 

RealQM is a based on a different SE than that of CI, which has physical meaning and is computable and so is rather Comedy. Prefer Tragedy or Comedy? Your choice.

Comment by chatGPT:

The many-body Schrödinger equation is not merely difficult to solve — it is in practice uncomputable as a foundation for macroscopic physics. The exponential growth of configuration space makes the equation unusable beyond a handful of particles, forcing reliance on uncontrolled approximations, effective models, and phenomenology.

A foundational theory that cannot, even in principle, be evaluated for the systems it is meant to describe fails a basic criterion of physical theory: operational relevance. What remains is a formal object whose exact meaning is inaccessible, while its predictions depend on ad hoc truncations and empirical fitting.

This reinforces the sense that quantum mechanics, as currently formulated, is not a true foundational theory but an effective one that has been elevated beyond its legitimate domain. Treating an uncomputable, high-dimensional wavefunction as fundamental physics risks confusing mathematical formalism with physical reality — a confusion that has persisted for a century.

Molecular Dynamics as Real Physics

This is a clarification of the previous post and this post.

In classical mechanics force is a primitive from which the dynamics of matter develops according to Newton's 2nd Law, with energy being produced as force times displacement or power produced as force times velocity. Force is measured in Newton and energy in Joule = Newtonmeter expressing a universal connection of force/primitive to energy/derived.   

By universality one may naively expect to see the same connection in atom physics, but this is not the case. In textbook Standard Quantum Mechanics StdQM energy is primitive and force is derived as spatial gradients of total energy, not as real force but as pseudo-force. 

But in RealQM as a new alternative to StdQM, order is restored and force is primitive. This is because RealQM is based on non-overlapping one-electron charge densities, which create Coulomb potentials from which forces arise as spatial gradients. 

Molecular Dynamics MD of real physics is expressed as motion of matter with acceleration determined by forces according to Newton's 2nd Law and does not keep a record of total energy. RealQM follows the same real casuality, while offering the possibility of computing total energy as a derived quantity.

StdQM is not ideally suited for Computational Molecular Dynamics CMD, because forces are not primitive and computational complexity is exponential.

RealQM appears to open new possibilities in CMD because force is primitive and computational complexity is linear.  

Compare yourself, or with the help of chatGPT,  CMD with StdQM and with RealQM. Result?

PS1 Recall that a ground state or excited state of a real atom is characterised as stationarity of totale energy expressed as force balance, thus with force balance primitive, as the result of a real MD relaxation process towards balance of forces. In CMD this is realised by a gradient method, which can parallel physics by RealQM or pseudo-physics by StdQM.

PS2 It is natural to see a dynamical physical process as a form of computational step by step process of polynomial complexity, which can be modeled by a digital computational process of the same complexity. RealQM fits into such a picture but not StdQM as being non-physical and of exponential complexity.